From image processing operations which entail identifying or authenticating a person, those based on the recognition of all or part of their face, such as facial recognition or iris recognition processing operations, are singled out. Identification and authentication are understood respectively as the determination and verification of the identity of the person. These processing operations normally comprise a step of acquisition of an image of the person, a step of localisation of his face and his eyes in the acquired image, a step of extraction of a model representing his biometric data on the basis of the positions of his eyes, and a step of comparison of the model with one or more other models representing given persons. For most of these image processing operations, the results of the step of extraction of the model representing biometric data of the person, notably in terms of error rates, depend largely on the precision of the determination of the positions of the eyes in the image. The algorithms for determining the position of an eye in an image generally provide approximate positions, notably if the image is acquired “on-the-fly”, i.e. without the cooperation of the person detected.